The faces are, if not the same, then similar. The smiling boys in the photographs look like each other and like teenage boys everywhere: eager, amused, naive. They are brimming with life. Except these four boys are dead. Naftali Frankel, Gilad Shaar and Eyal Yifrach were murdered first, their bodies found on Monday, and Mohamed Abu Khdeir was murdered after that, his life apparently taken in revenge for the other three. All four, the three Israelis and the Palestinian, have something in common besides those teenage smiles: their lives were ended by people capable of believing that to slaughter an innocent child is a noble act of service, somehow a good deed in the cause of the nation.

The dread thought now is that there will be more such people, Palestinians who feel it their sacred duty to avenge Mohamed's death by killing more blameless Israeli children. And that they will be followed by Israelis who feel compelled in the name of national pride or holy vengeance to snatch and kill another equally blameless Palestinian child. And on and on it will go.

When the suicide bombing was a grim novelty back in the 1990s, as Palestinian groups sent young men to detonate themselves on buses, in discos or pizzerias, it seemed the very depths of hell had been plumbed. What more vile act could there be? Yet the events of this week suggest a prospect no less bleak: a tit-for-tat cycle in which these two peoples snatch and murder their young.

Today, there was still no conclusive evidence that Hamas was behind the murder of the Israeli boys, just as it has not been proved that the Palestinian boy was the victim of extremist Jewish vigilantes. But that is what both sides believe, so that's what matters. Steadily, the driest, most combustible tinder is piling up.

Mohamed was abducted and killed from his home in East Jerusalem, the most contested place in a conflict where every inch is contested. It's the holy Muslim festival of Ramadan. In this climate, all it takes is one spark. The question haunting both sides is, could this week trigger the start of what would be a third intifada?

It's worth remembering the period that led to the outbreak of the second Palestinian uprising, in September 2000. It came after the very public failure of a peace process, at Bill Clinton's log cabin retreat of Camp David. When the breakthrough didn't come, it left behind not so much disappointment as a vacuum. In the absence of any diplomatic activity, the hardmen took over.

Expectations for John Kerry's peace initiative were much lower. Yet its collapse this spring was bound to have an effect. The lesson of Middle East diplomacy seems to be that failure does not send you back to square one: it sends you back several steps further. That could be what we are witnessing now, a diplomatic defeat that does not make things as bad as they were before but much worse.

That, incidentally, should give future would-be peacemakers, especially in the US, pause. The conventional wisdom always held that any initiative was better than none, that common sense dictated it was better for the two parties to be talking to each other than not. The experience of 2000 and perhaps 2014 suggests otherwise – that unless some of the underlying conditions that have led every past effort to fail have been addressed, a stagnant stalemate might be preferable to talks that begin only to end in disaster.What's more, a conflagration this time could be even more lethal than the one that broke out in 2000. For one thing, the regional climate has changed. The most murderous sectarian violence is taking place just over Israel's northern border in Syria, and beyond there in Iraq. On the other side stands a Jewish settler movement more aggressively messianist and bellicose than before. The evidence has been mounting for a while, in so-called price tag attacks on Palestinian property, designed to prove that any challenge to the settlement enterprise will exact a price, and in the regular assaults on Palestinian olive groves, uprooting trees that are centuries old.

Some of this settler fury is directed at the institutions of Israel itself, including the army, which the most extreme settlers now view as a hostile force. Until now, the settler leadership has usually been happy to stand behind and rely upon the Israeli state, confident that it has allies at the highest level, including in the cabinet, who will defend its interests and people. But the vigilante attack on Mohamed Abu Khdeir, if that's what it was, suggests another possibility: that settlers will increasingly take the law into their own hands.

Put simply, there are solid reasons to fear that a third intifada could be far more bloody than the uprisings that have gone before. Which means the task facing leaders on all sides could not be clearer: they have to calm this situation, not inflame it.

Some of the outward signs have not been encouraging. Despite reports of a truce between Hamas and Israel, the former's rockets kept on coming . And Israel has kept up its air strikes on Gaza. The rhetoric of Prime Minister Binyamin Netanyahu has hardly been designed to cool the fever. Perhaps he referred to the killers of the Israeli teenagers as "wild beasts" in order to reflect the rage he knew his countrymen felt, but it's always dangerous to imply an enemy is less than human, because it makes any action against that enemy legitimate. Mohamed Abu Khdeir was killed a matter of hours after Netanyahu spoke.

For all that, Israel and Hamas have both acted with more restraint than may be obvious. Backed by the cautious voices of Israel's military high command, Netanyahu has resisted demands made by the wilder members of his coalition, including for the re-conquest of Gaza, and so far seems determined to avoid escalation to all-out confrontation. It's worth noting the Israeli authorities acted swiftly to punish four soldiers who posted pictures of themselves calling for revenge, sentencing them to 10 days in military prison. For its part, Hamas has not unleashed the firepower everyone knows it has, including missiles that could reach Tel Aviv and beyond. The former Israeli intelligence chief who remarked that Hamas is no Isis is surely right.

Perhaps this is the best one can hope for, that the voices of sanity prevail. Among them should be that of Rachel Frankel, mother of 16 year-old Naftali, who, when she heard that a Palestinian teenager had been murdered in apparent revenge for her son, condemned it immediately. She broke into her own period of mourning to issue a statement: "There is no difference between blood and blood. Murder is murder. There is no justification and no atonement for murder." She knows that a teenage boy is just a teenage boy, and that a mother's tears taste the same – no matter who weeps them.